I311 implementation

I311 are implemented in DADOS as planar defects in {311} orientations, formed by interstitials arranged in parallel rows along <0-11> directions.

When a I311 is formed, its orientation is randomly chosen from the 12 equivalent {311} orientations.

The distance between rows is:

I311 are supposed to have an areal density of r = 5 interstitials / nm².

The distance between consecutive interstitials in the I311 is theoretically given theoretically by:

But, as it is experimentally known, only a 61 % of the rows are occupied. DADOS uses a higher value of dL in order to maintain the correct areal density keeping all the positions occupied. Thus, the distance between consecutive interstitials (in a row) is taken to be:

The total number of interstitials in the structure is n = n_L · n_W, where n_L is the number of interstitials per row and n_W is the number of rows.

I311 length: L = n_L · dL
I311 width: W = n_W · dW

The relation between width and lenght is assumed to be:

Taking into account above expressions, the number of rows of a given number of interstitials n will be

What DADOS does is to establish a threshold in the middle between two consecutive values for n_W. However, the values around this threshold are complicated to handle because small changes can yield a lot of changes in n_W. That is why DADOS implements a histeresis cycle, as shown in the figure:

Emission

I311s emit interstitials by taking one from the end of the row and releasing as a point defect it at any point randomly chosen in the surface. The emission rate is the same to the one described for clusters, and with the same binding energy:

Where:

• λ is the jump distance.

• D0ClusterProp is proportional to the prefactor.
• n is the cluster size.
• Eb is the binding energy.
• Em is the migration energy of the released point defect.
• See symbol list.

Growth

When a mobile interstitial is near enough to the I311 (closer than the capture distance), it is captured by it and is inserted into one of the ends of the defect (the closest one to the particle position).

The number of interstitials captures depends on the width: when the number of rows is reduced, then the structure gets a bigger length, and therefore, more captures will take place.

Shrinkage

When a mobile vacancy is near enough the I311 (closer than the capture distance), it is captured by it and it is recombined with an interstitial. When only one interstitial is remaining, the I311 is transformed into a point defect.